Quantum technology is pivotal to the future of physics, whether through quantum computing and simulation, or quantum sensing and measurement.All sorts of systems exhibit quantum phenomena and many different platforms are being developed for quantum information processing. Connecting these disparate quantum systems together is key to exploiting the advantages of each and growing the potential applications of quantum hardware. One of the most popular quantum computing platforms is superconducting qubits, using microwave-frequency electronics at cryogenic temperatures, which have promising results but are confined to operating within dilution refrigerators. In order to communicate through ambient environments, the ability to convert quantum signals between microwave electronics and infra-red fiber optics is highly sought after.Of the various approaches to this challenge, a promising candidate is optomechanical crystal resonators that use simultaneous photonic and phononic crystals to create a co-localized cavity coupling infra-red electromagnetic modes to microwave-frequency acoustic modes, which then via electromechanical interactions can undergo direct transduction to electronics. The majority of work in this area has been on one-dimensional nanobeam resonators which provide strong optomechanical couplings of gom ~ 1 MHz but, due to their geometry, suffer from an inability to dissipate heat produced by the laser pumping required for operation. Here we explore two-dimensional optomechanical crystal resonators, as structures with improved heat conduction properties, for their potential application in quantum microwave-electronic to infra-red optic transduction.Gallium arsenide is used as our material of choice due to its native piezoelectricity and favourable mechanical resonance frequencies. We conclude by adapting the vertebrae quasi-two-dimensional optomechanical resonator design to gallium arsenide and demonstrating a device with gom ~ 650 kHz.